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Stochastic averaging of strongly nonlinear oscillators with small fractional derivative damping under combined harmonic and white noise excitations

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Abstract

A stochastic averaging method for strongly nonlinear oscillators with lightly fractional derivative damping of order α (0<α<1) under combined harmonic and white noise external and (or) parametric excitations is proposed and then applied to study the first passage failure of Duffing oscillator with lightly fractional derivative damping of order 1/2 under combined harmonic and white noise excitations in the case of primary parametric resonance. Numerical results show that the proposed method works very well.

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Authors and Affiliations

  1. Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, 310027, China

    L. C. Chen & W. Q. Zhu

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  1. L. C. Chen
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  2. W. Q. Zhu
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Correspondence to W. Q. Zhu.

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Chen, L.C., Zhu, W.Q. Stochastic averaging of strongly nonlinear oscillators with small fractional derivative damping under combined harmonic and white noise excitations. Nonlinear Dyn 56, 231–241 (2009). https://doi.org/10.1007/s11071-008-9395-6

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